Lending Mortage Analysis
Exploratory Data Analysis
Marjorie Blanco, Joe Thompson, Haodi Tu
The data set contains 1989 records. The overall descriptive statistics:
## Married Meet credit history guidelines
## No : 678 0 : 171
## Unknown: 3 1 :1816
## Yes :1308 666: 2
##
##
##
## Other obligations as a percent of total income non-Hispanic Black
## Min. : 0.00 No :1792
## 1st Qu.:28.00 Yes: 197
## Median :33.00
## Mean :32.39
## 3rd Qu.:37.00
## Max. :95.00
## Hispanic Male Mortgage loan approved
## No :1878 No : 369 No : 244
## Yes: 111 Unknown: 15 Yes:1745
## Yes :1605
##
##
##
## Loan amount/purchase price Race
## Min. : 2.105 Hispanic : 111
## 1st Qu.: 70.000 non-Hispanic Black: 197
## Median : 80.000 non-Hispanic White:1681
## Mean : 77.064
## 3rd Qu.: 89.894
## Max. :257.143Descriptive statistics by Race:
## $Hispanic
## MARRIED GDLIN OBRAT MALE APPROVE
## No :31 0 :16 Min. :14.60 No :22 No :26
## Unknown: 1 1 :95 1st Qu.:29.00 Unknown: 2 Yes:85
## Yes :79 666: 0 Median :33.00 Yes :87
## Mean :33.46
## 3rd Qu.:38.45
## Max. :62.00
## LOANPRC RACE
## Min. : 39.39 Hispanic :111
## 1st Qu.: 80.00 non-Hispanic Black: 0
## Median : 89.39 non-Hispanic White: 0
## Mean : 85.17
## 3rd Qu.: 90.42
## Max. :162.63
##
## $`non-Hispanic Black`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 76 0 : 53 Min. : 5.60 No : 51 No : 64
## Unknown: 0 1 :144 1st Qu.:31.00 Unknown: 2 Yes:133
## Yes :121 666: 0 Median :35.00 Yes :144
## Mean :34.94
## 3rd Qu.:38.90
## Max. :63.00
## LOANPRC RACE
## Min. : 28.99 Hispanic : 0
## 1st Qu.: 80.00 non-Hispanic Black:197
## Median : 87.02 non-Hispanic White: 0
## Mean : 83.97
## 3rd Qu.: 90.24
## Max. :255.52
##
## $`non-Hispanic White`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 571 0 : 102 Min. : 0.00 No : 296 No : 154
## Unknown: 2 1 :1577 1st Qu.:27.60 Unknown: 11 Yes:1527
## Yes :1108 666: 2 Median :32.50 Yes :1374
## Mean :32.02
## 3rd Qu.:36.50
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 0
## 1st Qu.: 68.182 non-Hispanic Black: 0
## Median : 79.888 non-Hispanic White:1681
## Mean : 75.719
## 3rd Qu.: 89.623
## Max. :257.143
Descriptive statistics by Marital Status:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :678 0 : 64 Min. : 4.00 No :252 No :102
## Unknown: 0 1 :614 1st Qu.:28.00 Unknown: 7 Yes:576
## Yes : 0 666: 0 Median :33.00 Yes :419
## Mean :32.74
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 31
## 1st Qu.: 72.426 non-Hispanic Black: 76
## Median : 80.000 non-Hispanic White:571
## Mean : 77.967
## 3rd Qu.: 89.978
## Max. :162.626
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE LOANPRC
## No :0 0 :0 Min. :13.0 No :1 No :0 Min. : 86.96
## Unknown:3 1 :3 1st Qu.:23.3 Unknown:0 Yes:3 1st Qu.: 88.62
## Yes :0 666:0 Median :33.6 Yes :2 Median : 90.29
## Mean :27.2 Mean : 98.16
## 3rd Qu.:34.3 3rd Qu.:103.76
## Max. :35.0 Max. :117.24
## RACE
## Hispanic :1
## non-Hispanic Black:0
## non-Hispanic White:2
##
##
##
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 0 0 : 107 Min. : 0.00 No : 116 No : 142
## Unknown: 0 1 :1199 1st Qu.:28.00 Unknown: 8 Yes:1166
## Yes :1308 666: 2 Median :33.00 Yes :1184
## Mean :32.22
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 8.772 Hispanic : 79
## 1st Qu.: 68.857 non-Hispanic Black: 121
## Median : 80.000 non-Hispanic White:1108
## Mean : 76.547
## 3rd Qu.: 89.866
## Max. :257.143Descriptive statistics by Gender:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :252 0 : 31 Min. : 6.99 No :369 No : 50
## Unknown: 1 1 :338 1st Qu.:28.00 Unknown: 0 Yes:319
## Yes :116 666: 0 Median :33.00 Yes : 0
## Mean :32.64
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 11.01 Hispanic : 22
## 1st Qu.: 70.83 non-Hispanic Black: 51
## Median : 80.00 non-Hispanic White:296
## Mean : 77.66
## 3rd Qu.: 90.00
## Max. :255.52
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE
## No :7 0 : 0 Min. :24.00 No : 0 No : 0
## Unknown:0 1 :15 1st Qu.:29.95 Unknown:15 Yes:15
## Yes :8 666: 0 Median :34.50 Yes : 0
## Mean :33.33
## 3rd Qu.:37.65
## Max. :40.30
## LOANPRC RACE
## Min. :39.39 Hispanic : 2
## 1st Qu.:74.93 non-Hispanic Black: 2
## Median :75.42 non-Hispanic White:11
## Mean :75.59
## 3rd Qu.:80.43
## Max. :92.90
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 419 0 : 140 Min. : 0.00 No : 0 No : 194
## Unknown: 2 1 :1463 1st Qu.:28.00 Unknown: 0 Yes:1411
## Yes :1184 666: 2 Median :33.00 Yes :1605
## Mean :32.32
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 87
## 1st Qu.: 69.655 non-Hispanic Black: 144
## Median : 80.000 non-Hispanic White:1374
## Mean : 76.942
## 3rd Qu.: 89.881
## Max. :257.143There are 3 records are missing married (MARRIED) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 356 | Unknown | 1 | 35.0 | No | Yes | Yes | Yes | 86.95652 | Hispanic |
| 759 | Unknown | 1 | 33.6 | No | No | Yes | Yes | 90.28571 | non-Hispanic White |
| 1392 | Unknown | 1 | 13.0 | No | No | No | Yes | 117.24140 | non-Hispanic White |
There are 3 records are missing married (GDLIN) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 881 | Yes | 666 | 35 | No | No | Yes | Yes | 75.82939 | non-Hispanic White |
| 1229 | Yes | 666 | 26 | No | No | Yes | Yes | 100.00000 | non-Hispanic White |
There are 15 records are missing gender (MALE) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC | RACE |
|---|---|---|---|---|---|---|---|---|---|
| 1 | No | 1 | 34.5 | No | No | Unknown | Yes | 75.42373 | non-Hispanic White |
| 127 | No | 1 | 31.6 | No | No | Unknown | Yes | 80.80000 | non-Hispanic White |
| 286 | Yes | 1 | 37.3 | No | No | Unknown | Yes | 80.05337 | non-Hispanic White |
| 452 | Yes | 1 | 40.1 | Yes | No | Unknown | Yes | 75.00000 | non-Hispanic Black |
| 618 | Yes | 1 | 38.5 | No | No | Unknown | Yes | 92.90323 | non-Hispanic White |
| 695 | Yes | 1 | 25.0 | No | No | Unknown | Yes | 64.48276 | non-Hispanic White |
| 762 | Yes | 1 | 27.6 | No | No | Unknown | Yes | 75.55556 | non-Hispanic White |
| 768 | No | 1 | 35.6 | No | No | Unknown | Yes | 64.74397 | non-Hispanic White |
| 833 | Yes | 1 | 24.0 | No | Yes | Unknown | Yes | 79.80769 | Hispanic |
| 979 | No | 1 | 31.7 | No | No | Unknown | Yes | 74.86033 | non-Hispanic White |
| 1040 | No | 1 | 38.0 | Yes | No | Unknown | Yes | 75.38462 | non-Hispanic Black |
| 1070 | Yes | 1 | 40.3 | No | Yes | Unknown | Yes | 39.39394 | Hispanic |
| 1092 | Yes | 1 | 29.7 | No | No | Unknown | Yes | 90.10239 | non-Hispanic White |
| 1613 | No | 1 | 30.2 | No | No | Unknown | Yes | 90.00000 | non-Hispanic White |
| 1924 | No | 1 | 35.8 | No | No | Unknown | Yes | 75.32051 | non-Hispanic White |
## APPROVE
## RACE No Yes
## Hispanic 26 85
## non-Hispanic Black 64 133
## non-Hispanic White 154 1527
## APPROVE
## MARRIED No Yes
## No 102 576
## Unknown 0 3
## Yes 142 1166
## APPROVE
## MALE No Yes
## No 50 319
## Unknown 0 15
## Yes 194 1411
## , , RACE = Hispanic
##
## APPROVE
## MARRIED No Yes
## No 7 24
## Unknown 0 1
## Yes 19 60
##
## , , RACE = non-Hispanic Black
##
## APPROVE
## MARRIED No Yes
## No 27 49
## Unknown 0 0
## Yes 37 84
##
## , , RACE = non-Hispanic White
##
## APPROVE
## MARRIED No Yes
## No 68 503
## Unknown 0 2
## Yes 86 1022
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE +
## LOANPRC, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.53721 3.70447 -0.03525 -0.80680 -0.84499
## MALE1 LOANPRC
## 0.14139 -0.01643
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1965 Residual
## Null Deviance: 1476
## Residual Deviance: 966 AIC: 980## 2.5 % 97.5 %
## (Intercept) 0.39043496 2.703252996
## GDLIN1 3.29115094 4.137733306
## OBRAT -0.05549706 -0.015038547
## BLACK1 -1.26962817 -0.326297080
## HISPAN1 -1.42913599 -0.215005260
## MALE1 -0.30298683 0.565437899
## LOANPRC -0.02663168 -0.006658542## 2.5 % 97.5 %
## (Intercept) 0.38363811 2.690789543
## GDLIN1 3.28199418 4.126951904
## OBRAT -0.05547873 -0.015022012
## BLACK1 -1.27779072 -0.335818281
## HISPAN1 -1.45043209 -0.239548275
## MALE1 -0.29193829 0.574720492
## LOANPRC -0.02635892 -0.006504892## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1 MALE1
## 4.6516120 40.6286322 0.9653637 0.4462819 0.4295616 1.1518751
## LOANPRC
## 0.9837024## OR 2.5 % 97.5 %
## (Intercept) 4.6516120 1.4776234 14.9282142
## GDLIN1 40.6286322 26.8737761 62.6606279
## OBRAT 0.9653637 0.9460148 0.9850740
## BLACK1 0.4462819 0.2809361 0.7215908
## HISPAN1 0.4295616 0.2395158 0.8065372
## MALE1 1.1518751 0.7386088 1.7602184
## LOANPRC 0.9837024 0.9737198 0.9933636
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.66644 3.69659 -0.03524 -0.81891 -0.84836
## LOANPRC
## -0.01652
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1966 Residual
## Null Deviance: 1476
## Residual Deviance: 966.4 AIC: 978.4##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE +
## LOANPRC, family = binomial(link = "probit"), data = data)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.64766 2.13928 -0.01705 -0.42091 -0.43124
## MALE1 LOANPRC
## 0.06307 -0.00827
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1965 Residual
## Null Deviance: 1476
## Residual Deviance: 965.5 AIC: 979.5## Overall
## GDLIN1 17.7034125
## OBRAT 3.1949750
## BLACK1 3.3211862
## HISPAN1 2.6512623
## MALE1 0.5695835
## LOANPRC 3.2178042##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = binomial(link = "probit"), data = data)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.706553 2.136046 -0.017060 -0.427179 -0.432845
## LOANPRC
## -0.008317
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1966 Residual
## Null Deviance: 1476
## Residual Deviance: 965.8 AIC: 977.8## Overall
## GDLIN1 17.702452
## OBRAT 3.197948
## BLACK1 3.383556
## HISPAN1 2.662084
## LOANPRC 3.236990## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1965 965.48
## 2 1966 965.80 -1 -0.3199 0.5717## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 7 -482.74
## 2 6 -482.90 -1 0.3199 0.5717##
## Call: glm(formula = APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC,
## family = binomial(link = "probit"), data = data)
##
## Coefficients:
## (Intercept) GDLIN1 BLACK1 HISPAN1 MALE1
## 0.105974 2.184604 -0.441909 -0.441348 0.064210
## LOANPRC
## -0.009121
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1966 Residual
## Null Deviance: 1476
## Residual Deviance: 977.2 AIC: 989.2## Overall
## GDLIN1 18.2133105
## BLACK1 3.4982924
## HISPAN1 2.7352593
## MALE1 0.5837877
## LOANPRC 3.6344426## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1965 965.48
## 2 1966 977.18 -1 -11.697 0.0006261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 7 -482.74
## 2 6 -488.59 -1 11.697 0.0006261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call: glm(formula = APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC, family = binomial(link = "probit"),
## data = data)
##
## Coefficients:
## (Intercept) GDLIN1 BLACK1 HISPAN1 LOANPRC
## 0.165274 2.181533 -0.448539 -0.443199 -0.009168
##
## Degrees of Freedom: 1971 Total (i.e. Null); 1967 Residual
## Null Deviance: 1476
## Residual Deviance: 977.5 AIC: 987.5## Overall
## GDLIN1 18.213136
## BLACK1 3.565111
## HISPAN1 2.748035
## LOANPRC 3.654179## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1965 965.48
## 2 1967 977.52 -2 -12.033 0.002438 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 7 -482.74
## 2 5 -488.76 -2 12.033 0.002438 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
